Magnetic anisotropy of FePt nanoparticles: temperature-dependent free energy barrier for switching

Abstract

We report the calculation of free energy with constrained magnetization for $lo$ FePt nanoparticles. We employ effective spin Hamiltonian model constructed on the basis of constrained density functional theory calculations for $lo$ FePt. In this model the Fe spins (treated as classical spins in this work) are coupled "directly" and via induced Pt moments with both isotropic and anisotropic interactions. Interactions mediated by the Stoner enhanced Pt moment stabilize ferromagnetic order and lead to a pronounced coordination dependence and long-range interactions. The free energy of these nanoparticles, as a function of the temperature and the constrained magnetization $F(T,M_z)$, is calculated from the joint density of states $g(E,M)$, using the extended Wang-Landau algorithm. The free energy barrier for magnetization reorientation is found to depend fairly linearly on the temperature in the ferromagnetic phase and vanishes in the paramagnetic phase.